If `f: R->R` is an odd function such that `f(1+x)=1+f(x)`and `x^2f(1/x)=f(x),x!=0` then find `f(x)dot`

If f: R^+ to R , f(x) + 3x f(1/x)= 2(x+1),t h e n find f(x)

Let f(x) be a continuous function such that f(0) = 1 and f(x)=f(x/7)=x/7 AA x in R, then f(42) is

Let f: R^+ ->R be a function which satisfies f(x)dotf(y)=f(x y)+2(1/x+1/y+1) for x , y > 0. Then find f(x)dot

If f:R->R is a twice differentiable function such that f''(x) > 0 for all x in R, and f(1/2)=1/2 and f(1)=1, then

If f:R rarr R is a function such that f(5x)+f(5x+1)+f(5x+2)=0, AA x in R , then the period of f(x) is

If f: R->R is an invertible function such that f(x) and f^-1(x) are symmetric about the line y=-x, then (a) f(x) is odd (b) f(x) and f^-1(x) may be symmetric (c) f(c) may not be odd (d) none of these

If f(x)=a x^2+b x+c is a quadratic function such that f(1)=8,f(2)=11 and f(-3)=6 find f(x) by using determinants. Also, find f(0)dot

Let f : R to R be a function such that f(0)=1 and for any x,y in R, f(xy+1)=f(x)f(y)-f(y)-x+2. Then f is

Let a function f(x), x ne 0 be such that f(x)+f((1)/(x))=f(x)*f((1)/(x))" then " f(x) can be

Let a function f(x) satisfies f(x)+f(2x)+f(2-x)+f(1+x)=x ,AAx in Rdot Then find the value of f(0)dot